A C172 SINGLE PLT VIOLATED R-531 WHEN IN FAY'S AIRSPACE.

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IT WAS OUR FIRST TRIP TO RAEFORD. OUR TRIP TO RAEFORD WAS UNEVENTFUL; HAD MAINTAINED CONTACT WITH FAYETTEVILLE APCH TO AVOID AREA R-531. RETURN FLT WAS IN THE DARK. I CONDUCTED THE RUN-UP ON THE RAMP AS PK AIRPARK HAS NO TXWY AND COMPLETED THE BEFORE TKOF CHKLIST THERE. I REMEMBER SPECIFICALLY SETTING THE HDG INDICATOR BEFORE BACK-TAXIING TO RWY 4 FOR DEP. BECAUSE OF THE UNFAMILIAR ARPT; SIT; AND CIRCUMSTANCES (MY 2 CHILDREN WERE IN THE BACK OF THE PLANE); I NEGLECTED MY USUAL 'LIGHTS (BEACON; NAV); CAMERA (XPONDER); ACTION (THROTTLE) CHKLIST. AS SOON AS WE WERE 1000 FT AGL; I TURNED US DUE W; A HDG WHICH SHOULD HAVE TAKEN THE PLANE DIRECTLY OVER MACKALL; A CLASS D AIRSPACE WITH TOP AT 2900 FT; AND BEGAN CLBING TO 3000 FT. AT THIS POINT; I CONTACTED FAYETTEVILLE APCH; WHO GAVE US A XPONDER CODE AND INFORMED US TO STAY OUT OF CLASS C AIRSPACE. AT 2500 FT MSL; I REALIZED THE XPONDER WAS ON 'STANDBY' AND TURNED IT TO 'ALT.' A FEW MOMENTS LATER; FAYETTEVILLE INFORMED ME I WAS 1 MI INSIDE R-531 AND ASSIGNED ME A HDG OUT OF THE AIRSPACE. ONCE OUT OF THE AIRSPACE; I DOUBLECHKED ALL MY INSTS AND DISCOVERED MY HDG INDICATOR WAS PRECESSED MORE THAN 40 DEGS. I HAD UNWITTINGLY HEADED N. I CORRECTED THE ERROR. THE FLT TERMINATED AT TTA ARPT WITHOUT FURTHER INCIDENT.